Not necessarily; some airports are closed at night to keep nearby residents happy. If you're operating a hub-and-spoke airline out of such an airport, there's not much activity going on at night. There's still some; your longhaul flights are still there, so the NOC is likely still open, but there's far less activity than you'd have during the day.

there's a lull from 1am - 5am as pilots are sleeping and airports are dormant. It kicks back up again at 5am for the early bird flights. Aircraft parked at the gates will be powered down for the night only to be brought back to life a few hours later. Southwest isn't a major international airline so you won't find them flying 24/7 like Delta or Lufthansa.